Functions f(x) and g(x) are both increasing. in addition, the range of g is in domain of f. prove that composite function f(g(x)) is increasing

F: D -> E;
g: F -> G, where, g(F) is in D;

Let be x1, x2 ∈ F, with x1 < x2;
But, g(x1) < g(x2), because g is increasing; => f(g(x1) < f(g(x2) , because f is increasing =>
f(g(x) is increasing.